The Spain international was shown a straight red card 10 minutes into the second half at the Nou Camp after yelling in the face of the assistant referee, an action he later apologised for on Twitter.
The La Liga giants were attempting to overturn a 4-0 deficit from the first leg against Athletic Bilbao, but could only manage a 1-1 draw, missing out on the Super Cup trophy.
Referee Carlos Velasco Carballo wrote in his post-match report that Pique had used insulting language to his assistant, which the player later refuted in a statement.
Writing on Twitter on Tuesday, Pique said: “I want to apologise because the attitude with which I protested to the assistant referee was not the correct one.
“It was a very tense match with a lot at stake. However, at no point did I direct any insult towards him.”
Despite the apology, the Spanish soccer federation (RFEF) have decided to issue a four-game ban which will see the experienced centre-back miss the start of Barcelona’s season.
The champions begin their La Liga title defence against Athletic Bilbao on Sunday, bidding to win their sixth league title in eight years.